This invention relates to a nuclear magnetic resonance imaging (hereinafter referred to as the "MRI") apparatus for measuring nuclear magnetic resonance (hereinafter referred to as the "NMR") signals from hydrogen, phosphorus, etc., in an object under inspection and imaging a distribution of a nuclear spin density, a distribution of the time of relaxation, etc., and to an image reconstruction method in the nuclear magnetic resonance imaging apparatus for reconstructing and imaging detected data of MRI.
MRI is a method which determines a spatial distribution of NMR parameters by encoding position data to the NMR signals and displaying it as an image, and it is known that a reconstructed image can be obtained by performing Fourier transform on the detected data in MRI ("NMR in Medicine", pp. 129-130, Maruzen (1991) and "Illustrative MRI", pp. 145-147, Shujunsha (1991)). In MRI, the NMR signal is measured at each discrete point of an acquired data space (which is called a "Fourier space" or a "k space") having a phase encode direction and a frequency encode direction as coordinates axes thereof. At this time, encode is applied in each of the phase encode direction and the frequency encode direction in an imaging sequence for detecting the NMR signals, and the NMR signals are detected. In such measurement, an imaging method is known which does not measure a part of regions in either one of the phase encode direction and the frequency encode direction but estimates data of undetected regions by mathematical processing and reconstructs an image. This imaging method is called under the name of a "half Fourier method", a "half scan method" when a part of the undetected regions exists in the phase encode direction or a "half echo method" when a part of the undetected regions exists in the frequency encode direction. Hereinafter, these imaging methods will be generically referred to as the "half imaging method".
The image reconstructed by Fourier transform of the detected data of MRI corresponds to tomograph of the object and is also referred to as the "density distribution". Hereinafter, the image thus reconstructed will be referred to merely as the "reconstructed image". If the reconstructed image is a real number, complex conjugate symmetry is ideally established in the MRI detected data as the Fourier transform of the reconstructed image ("NMR in Medicine", pp. 134-135 (Maruzen, 1991)). In practical MRI, however, this complex conjugate symmetry is no longer established due to inhomogeneity of a static magnetic field, inhomogeneity of a magnetic field induced depending on a permeability distribution of the object and other causes inherent to apparatus characteristics, and the reconstructed image becomes a complex image. Accordingly, a specific calculation method for estimating undetected data becomes necessary in order to obtain excellent reconstructed images in the half imaging method. As this calculation method, "The Journal of the Institute of Electronics, Information and Communication Engineers, Transaction on Communications D", Vol. J71-D, No. 1, pp. 182-187 and "Journal of the Society and Control Engineers", Vol. 30, No. 9, pp. 818-827, and U.S. Pat. Nos. 4,780,675 and 4,912,413 describe a method of obtaining an excellent reconstructed image by estimating phase components of the reconstructed image to obtain a phase map, correcting the detected data by this phase map to obtain complex conjugate symmetry and estimating the undetected data. Furthermore, JP-A-62-8747 discloses another method, but quality of the image obtained by this method is inferior to that of the reconstructed image obtained by the method using the phase map.